One athlete in a race running on a long, straight track with a constant speed v1 is a distance d behind a second athlete running with a constant speed v2. (a) Under what circumstances is the first athlete able to overtake the second athlete? (b) Find the time t it takes the first athlete to overtake the second athlete, in terms of d, v1, and v2. (c) At what minimum distance d2 from the leading athlete must the finish line be located so that the trailing athlete can at least tie for first place? Express d2 in terms of d, v1, and v2 by using the result of part (b).

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(a)

In order to overtake the second athlete, the speed of the first
athlete must be greater than that of the second athlete. The
distance between second athlete and finishing line must be
reasonable to overtake. If the distance between second athlete and
finishing line is less, then first athlete cannot overtake the
second athlete.